[time 539] Re: [time 535] Chu Spaces & Construction by Games

Stephen P. King (stephenk1@home.com)
Fri, 13 Aug 1999 17:38:23 -0400

Dear Matti and Friends,

Matti Pitkanen wrote:
> On Fri, 13 Aug 1999, Stephen P. King wrote:
> > I see "structure" or pattern recognition as a general type of
> > bisimulation. I believe that this is modeled by Pratt then he discusses
> > Chu spaces with K > 2 values. For K = 2, we have a binary situation like
> > you ask: "familiar" or "unfamiliar", but this is easily seen to be vague
> > as it tacitly assumes an absolute "standard" to distinguish the two...
> > He proposes that QM can be represented by the behavior of Chu_K = C (C
> > being the set of complex numbers)...
> Interesting situation occurs when binary numbers Z_2 are replaced
> with G(p,1): finite field with p elements. What one obtains
> by the construction taking it to infinite is p-adic numbers with
> norm not larger than one: also p-adic numbers infinite as
> ordinary integers are included. Binary case would give 2-adics.
> What differentiates between this construction and construction of surreals
> is presumably that p-adic topology is introduced.
> > I think that the Pinary tree is a better model since it captures
> > phylogenetic relations that a binary tree can not! Thus the "history" of
> > a particular player has an effect on the possible moves it will make in
> > a particular game... We skew (?)or weigh the moves as a function of the
> > number of times that a particular move was successful for that player!?
> > Since Chu spaces represent both the games and the players of the games,
> > we can identify a player with a set of games and a game by an antiset of
> > players. (I think, I may be misinterpreting Pratt!?)

        BTW, a game between two players (chu spaces) A and B is defined by the
tensor product of A and B, which can be considered as a player of a
"bigger" game... See pg. 5,6 of ratmech.ps

> > You make a very good point here, but I believe that Dennett is mistakes
> > in thinking that the difference between, say "files of numbers" and the
> > "mechanism of the reading head" are only differences in *degree* and
> > that this is all there is to be said of the situation. If we are
> > strictly talking about the information content of the physical
> > embodiments of these informational structures, we can see that the
> > difference in only in degree, but Dennett's material monism blinds him
> > to the categorical difference in *kind* that exists between the "mental
> > object" (information about) A* and the physical object A.
> Yes, I understand you point.
> > > Isn't the situation same in physics? To take example relating to previous
> > > discussions. Could it be that spacetime geometry is tacit information?
> > > The dynamics of spacetime surface defined Kahler action as dynamical
> > > principle is tacit information not allowing representation in terms
> > > of LS interactions: simply because it defines these interactions!?
> > > Same would apply to unitary time evolution U: it would also represent
> > > 'raw physics'. Explicit (DNA, short term memory?) and potentially
> > > explicit (motor program in my brain realized as cascades of selves, long
> > > term memory realized in terms of self hierachy and communication between
> > > levels of hierarchy?) information would emerge only at the level when
> > > selves emerge.
> > Given my comment above, I agree with you here! :-) (Does Dennett allow
> > for "implicit" as the complement of "explicit"? I have read his book,
> > but I can't remember...)
> Probably: I think he divided implicit to potentially explicit and tacit.
> (I read a paper about implicit learning yesterday and found the
> definitions there).

        Could you send me the bibliodata on it?
> > In Hitoshi's LS theory, the "outsides" of LS are "physical" and the
> > "insides" are "mental", I think!? We could categorize the information
> > involved in the external behavior of LS in the way you describe here.
> > :-)
> I read the rathmech in train and I think I understand the general
> idea and philosophy. Although the basic philosophy is quite different
> from my stubborn beliefs, I find the mathematical idea beautiful. I hope
> I could apply it in my own thought constructions. To put
> it mildly, I am still far from any concrete model for cognitive
> representations: in any case, cognitive spacetime sheets and material
> spacetime sheets could replace mind and matter in TGD framework.
> Perhaps the models provided by cognitive spacetime sheets for the
> behaviour of material ones could be formulated in terms of
> Chu pair somehow defined by cognitive and material spacetime sheet forming
> self and K valued mapping |= would characterize the simulation
> provided by cognitive spacetime sheet for the behaviour of material
> one. Something like this...

        I have thought of your "cognitive and material spacetime sheets" as
representable by Chu spaces! :-) The |= can be interpreted as the
"payoff matrix of a von-Neumann-Morganstern two-person game"; it is a
matrix whose entries range over the values of K... How this applies to
your thought here I am not sure... The "self" is a "player" of the
"information acquisition game" that I see bisimulation to be.
> What troubles me that that the causation from mental to material
> was replaced by a K-valued function. And interpretation
> of the values of |= as complex time or logical value.
> If K=Z_2 this everything is ok but
> K=C? I did not quite understand the construction of left and
> right residuations in case of QM.
> I understood right residuation in general case.

        No, causation is not "replaced by a K-valued function", as I understand
it, it is a matrix of relations. Look at the 4th paragraph on pg. 3, 4th
paragraph of page 6, 3rd & 6th paragraph of pg. 8, 8th paragraph of pg.
9 of ratmech.ps, for various discussions of causality.
        The last reference is particularly telling: "...we find that two
events, or two states, communicate with each other by interrogating
*all* entities of the opposite type. Thus event a deduces that it
precedes event b not by broaching the matter with b directly, but
instead by consulting the record of every state to see if there is any
state volunteering a counterexample. When none is found, the precedence
is established. Conversely when a Chu space is in state x and desires to
pass to state y, it inquires as to whether this would undo any event
that has already occurred. If not then the transition is allowed."
        I am arguing that Pratt's idealized definition, presented here, can be
weakened to take into account computational error, entropy and the
"duration" or "granularity" of a transition, which is equivalent to your
q-jump. I am have only philosophical arguments and not mathematical ones
so I beg your patience and ask for your help to formalize the idea.
(Hint: entropy is generated in computing by erasing memory)
        I think that we need to also read
http://boole.stanford.edu/chuguide.html#ph94 to see more of Pratt's
ideas of how the construction works for QM. He does identify, on pg. 10
of ratmech.ps, right residuation with the inner product of a "mixed
state" and left residuation with the outer product.

> Chu spaces involve the
> assumption about *given* spaces A and X: isn't this assumption
> very similar to the assumption 'spacetimes are 4-surfaces
> of 8-dimensional H', which assumption in turn induces
> the concept of configuration space and its spinor structure
> crucial for quantum theory?

        I am not sure that we could really say "*given*", remember that there
is no notion of absolute initiality (or finality) of the spaces A and X,
they are constructed by constructions which are constructed themselves.
We are no longer using the naive classical notion that there is an
absolute "beginning" to a space. This notion can be see to derive from
the way that observations ("results of information acquisition games" in
Frieden's thinking and "the tensor product of Chu spaces" representing
observers in Pratt's thinking). An observation is a finite sampling,
like Robert Fung's "bucket" that scoops up a finite distribution of
spectra. Umm, I am not clearheaded right now, I'll try to elaborate more
on this some other time.



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